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We explore analytically and numerically agglomeration driven by advection andlocalized source. The system is inhomogeneous in one dimension, viz. along thedirection of advection. We analyze a simplified model with mass-independentadvection velocity, diffusion coefficient, and reaction rates. We also examinea model with mass-dependent coefficients describing aggregation withsedimentation. For the simplified model, we obtain an exact solution for thestationary spatially dependent agglomerate densities. In the model describingaggregation with sedimentation, we report a new conservation law and develop ascaling theory for the densities. For numerical efficiency we exploit thelow-rank approximation technique; this dramatically increases the computationalspeed and allows simulations of large systems. The numerical results are inexcellent agreement with the predictions of our theory.

Aggregation in non-uniform systems with advection and localized source